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Overview

This book is an introduction to Csub*-algebras and their representations on Hilbert spaces. The presentation is as simple and concrete as possible; the book is written for a second-year graduate student who is familiar with the basic results of functional analysis, measure theory and Hilbert spaces. The author does not aim for great generality, but confines himself to the best-known and also to the most important parts of the theory and the applications. Because of the manner in which it is written, the book should be of special interest to physicists for whom it opens an important area of modern mathematics. In particular, chapter 1 can be used as a bare-bones introduction to Csub*-algebras where sections 2.1 and 2.3 contain the basic structure thoery for Type 1 von Neumann algebras.

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Anonymous

Posted September 8, 2002

Invitation to C*-Algebras

Even though the book first appeared some years back, it is as useful now as ever. Students and others will always need a friendly entry point to any given subject: "Operator algebras! Oh, right! That is Arveson's book, isn't it?"--From a typical conversation I would have with a colleague from the other end of campus.-- Or, an impatient student, I meet in the elevator, wants to quickly get an idea of what it is all about,-- and have fun reading about the material, at the same time: That would be Arveson's lovely little book!-- Sure, there *are* lots of great books in the subject; but they haven't had this same kind of wide impact. The central ideas are very attractively presented: It *is* an invitation! The other books in C*-algebra theory will typically be thicker, and they might be more narrowly focused, --more for the specialists, if you like. The first edition of Arveson's book is from the seventies; but still,-- now many years later, everyone knows "An invitation", and reads it. Authors keep immitating its approach and its style: You see immitators,--authors in other specialties of math writing books entitled "An invitation to ...". But none of the immitations seem to have quite the charm of the original. You can't very well **plan to** write a charming book in math. But when one arrives, we all know it. The subject of Arveson's book started with quantum theory, Hilbert space, spectral theory, and representations of groups and algebras. And, in the half century plus, since its inception, the subject has found applications in a surprisingly wide range of other fields: geometry, K-theory, fundamental physics, symbolic dynamics, and tiling theory, to mention just a few.--A book which will not collect dust on the shelf!

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Anonymous

Posted September 2, 2002

Invitation to C*-Algebras

"Operator algebras! Oh, right! That is Arveson's book, isn't it?"--From a typical conversation I would have with a colleague from the other end of campus.-- Or, an impatient student, I meet in the elevator, wants to quickly get an idea of what it is all about,-- and have fun reading about the material, at the same time: That would be Arveson's lovely little book!-- Sure, there *are* lots of great books in the subject; but they haven't had this same kind of wide impact. The central ideas are very attractively presented: It *is* an invitation! The other books in C*-algebra theory will typically be thicker, and they might be more narrowly focused, --more for the specialists, if you like. The first edition of Arveson's book is from the seventies; but still,-- now many years later, everyone knows "An invitation", and reads it. Authors keep immitating its approach and its style: You see immitators,--authors in other specialties of math writing books entitled "An invitation to ...". But none of the immitations seem to have quite the charm of the original. You can't very well **plan to** write a charming book in math. But when one arrives, we all know it. The subject of Arveson's book started with quantum theory, Hilbert space, spectral theory, and representations of groups and algebras. And, in the half century plus, since its inception, the subject has found applications in a surprisingly wide range of other fields: geometry, K-theory, fundamental physics, symbolic dynamics, and tiling theory, to mention just a few.

Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.